In product development processes, CAE is utilized to reduce development costs and shorten design and development periods. In CAE, an analysis model is created from a shape model or the like generated on a CAD (computer aided design) system, and strength analysis, thermal analysis, vibration analysis or the like is carried out using an analysis method, for example, the finite element method or the boundary element method, with that analysis model. In the generation of an analysis model in CAE as described above, first, the work of creating a mesh model from a shape model and setting boundary conditions or the like on each element of the mesh model is required, and a lot of time and effort is needed particularly to create a mesh model. This is because, in an analysis method such as the finite element method, a solution changes depending on the size of the mesh (mesh size) and the user needs to find out an appropriate mesh size based on trial and error. Generally, analysis accuracy is improved as the mesh size is reduced. Meanwhile, as the mesh size decreases, computation scale increases and therefore analysis time increases. That is, analysis accuracy and analysis time are in a tradeoff relation.
A designer or person in charge of the analysis who is skilled in analysis intuitively grasps this tradeoff relation based on experience and therefore depends on empirical values though the person can decide an appropriate mesh size after some trials and errors. On the other hand, a beginner of analysis needs many trials and errors in order to decide an appropriate mesh size. Moreover, it is possible not only to set a uniform mesh size for an analysis target model but also to provide partly different mesh sizes (controlled mesh size density). Deciding an appropriate mesh size in consideration of this controlled mesh size density is not easy even to a person skilled in analysis.
In view of such backgrounds, techniques to reduce the burden of mesh creation are proposed.
JP-A-2005-018403 discloses a technique in which the degree of an element with a large error (low analysis accuracy) in a computation process is raised with respect to a created mesh, thus minimizing the error (improving analysis accuracy) (this method is called adaptive p-method).
JP-A-11-25292 discloses a technique in which a regular and fine mesh is generated in a portion designated as an evaluation part, thus creating a mesh with high quality, that is, a mesh with high analysis accuracy.
JP-A-6-259404 discloses a technique in which an error in an analysis result is evaluated, an element with an error equal to or greater than a reference value and peripheral elements thereof are deleted, and the resulting space is filled with a dense element. This process is repeated until the error is reduced to the reference value or below. Thus, a mesh with accuracy guaranteed is created.
JP-A-2006-4259 discloses a technique in which the relation between computer performance and analysis time and the relation between the number of divisions (mesh size) and analysis accuracy are stored in advance and analysis time and analysis accuracy are predicted based on these relations.
As described above, CAE has the problem that the burden of mesh creation needs to be reduced. To solve this problem, in the techniques of JP-A-2005-018403 and JP-A-6-259404, a mesh with high analysis accuracy is created by adjusting the degree of an element or the mesh size and thus minimizing an error. Therefore, the mesh size adjustment work through trial and error by the user is no longer necessary. However, in these techniques, since repetition of arithmetic operations to adjust the degree of an element or the mesh size takes place, there is a problem that the analysis calculation time per analysis is long. Generally, if a mesh that can be analyzed with accuracy equivalent to an analysis result by the p-method is created and normal analysis calculation is carried out, this analysis takes a calculation time approximately five times longer than in the p-method. When an analysis is carried out once to several times as in analysis to confirm a phenomenon, this approximately five times longer calculation time is significantly shorter than the time for trial and error of mesh size and is therefore practical. However, when an analysis is carried out tens to hundreds of times in order to find out design sensitivity or for optimized calculation or the like, there is a problem that the approximately five times longer calculation time is longer than the time for trial and error of mesh size.
In the technique of JP-A-11-25292, a regular and fine mesh is generated in a portion designated as an evaluation part, thus creating a mesh with high quality, that is, a mesh with high analysis accuracy. However, this technique only creates a mesh with relatively high analysis accuracy. Therefore, there is a problem that the technique does not create a mesh with sufficient accuracy guaranteed.
In the technique of JP-A-6-259404, as in the technique of JP-A-2005-018403, repetition of arithmetic operations takes place, prolonging the analysis calculation time. Therefore, when an analysis is carried out tens to hundreds of times, there is a problem that the calculation time needs to be shortened.
The technique of JP-A-2006-4259 has a problem that the user needs to prepare a mesh with accuracy guaranteed in advance.